Synopses & Reviews
The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.
Review
From the reviews: MATHEMATICAL REVIEWS "It is valuable both as an advanced graduate level text and as a reference for researchers?he book can be most strongly recommended."
Review
From the reviews:
MATHEMATICAL REVIEWS
"It is valuable both as an advanced graduate level text and as a reference for researchers?he book can be most strongly recommended."
Synopsis
There has been much demand for the statistical analysis of dependent ob- servations in many fields, for example, economics, engineering and the nat- ural sciences. A model that describes the probability structure of a se- ries of dependent observations is called a stochastic process. The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA) processes. We deal with a wide variety of stochastic processes, for example, non-Gaussian linear processes, long-memory processes, nonlinear processes, orthogonal increment process- es, and continuous time processes. For them we develop not only the usual estimation and testing theory but also many other statistical methods and techniques, such as discriminant analysis, cluster analysis, nonparametric methods, higher order asymptotic theory in view of differential geometry, large deviation principle, and saddlepoint approximation. Because it is d- ifficult to use the exact distribution theory, the discussion is based on the asymptotic theory. Optimality of various procedures is often shown by use of local asymptotic normality (LAN), which is due to LeCam. This book is suitable as a professional reference book on statistical anal- ysis of stochastic processes or as a textbook for students who specialize in statistics. It will also be useful to researchers, including those in econo- metrics, mathematics, and seismology, who utilize statistical methods for stochastic processes.
Table of Contents
Elements of Stochastic Processes.- Local Asymptotic Normality for Stochastic Processes.- Asymptotic Theory of Estimation and Testing for Stochastic Processes.- Higher Order Asymptotic Theory and Differential Geometry for Stochastic Processes.- Asymptotic Theory for Long-memory Processes.- Statistical Analysis Based on Functionals of Spectra.- Discriminant Analysis for Stationary Time Series.- Large Deviation Theory and Saddlepoint Approximation for Stochastic Processes.